Emergence of local synchronization in neuronal networks with adaptive couplings

Local synchronization, both prolonged and transient, of oscillatory neuronal behavior in cortical networks plays a fundamental role in many aspects of perception and cognition. Here we study networks of Hindmarsh-Rose neurons with a new type of adaptive coupling, and show that these networks naturally produce both permanent and transient synchronization of local clusters of neurons. These deterministic systems exhibit complex dynamics with 1/fη power spectra, which appears to be a consequence of a novel form of self-organized criticality

Asymmetric division coordinates collective cell migration in angiogenesis

The asymmetric division of stem or progenitor cells generates daughters with distinct fates and regulates cell diversity during tissue morphogenesis. However, roles for asymmetric division in other more dynamic morphogenetic processes, such as cell migration, have not previously been described. Here we combine zebrafish in vivo experimental and computational approaches to reveal that heterogeneity introduced by asymmetric division generates multicellular polarity that drives coordinated collective cell migration in angiogenesis. We find that asymmetric positioning of the mitotic spindle during endothelial tip cell division generates daughters of distinct size with discrete ‘tip’ or ‘stalk’ thresholds of pro-migratory Vegfr signalling. Consequently, post-mitotic Vegfr asymmetry drives Dll4/Notch-independent self-organization of daughters into leading tip or trailing stalk cells, and disruption of asymmetry randomizes daughter tip/stalk selection. Thus, asymmetric division seamlessly integrates cell proliferation with collective migration, and, as such, may facilitate growth of other collectively migrating tissues during development, regeneration and cancer invasion

Complex Networks: Structure and Dynamics

In this dissertation, we present a study of complex systems with underlying network topology. Complex systems are formed due to multiple interactions among many different elements. The interactions among the elements not only changes the properties of individual element but also guides them to self-organize. Implications of understanding both the functional and the structural aspects would be felt in a wide range of problem involving social interactions, neural process, disease spread, genome assembly and many more. Three research problems are addressed here: (A) structure of evolving networks; (B) emergence of fairness on complex networks which is understanding dynamics on a given network; and (C) modular synchronization which investigates evolution of network structure based on dynamics. A: It is now well established that complex networks share common properties in terms of their non-trivial network structure known as the network topology. We presented a statistical explanation for widely occurring complex network topologies with the assumption that the effect of various attributes, which determine the ability of each node to attract other nodes, is multiplicative. This composite attribute or fitness is shown to be lognormally distributed and is used in forming the complex network. By varying the parameters of the lognormal distribution, this construction generates many types of real-world networks.B: In the cortex of neural network, for instance, the neurons exhibit collective synchronization within each module rather than global synchronization. To explain this important phenomenon, we consider a well-connected network of neurons, each of which is described by the Hindmarsh-Rose model. The neurons in the system were coupled using adaptive coupling. Numerical simulations on the network demonstrates that modular synchronization emerges in a self-organized fashion.C: Understanding the emergence of fairness is crucial in many biological and social systems. Previous theoretical studies using the evolutionary ultimatum game do not explain the observed experimental behavior. We model this phenomenon using an ultimatum game with a nonlinear utility function. Our study of the game on complex networks show good agreement with the experiments. We also show that the clustering in the network and the nonlinear utility function play important roles in predicting the outcome

The temporal basis of angiogenesis

The process of new blood vessel growth (angiogenesis) is highly dynamic, involving complex coordination of multiple cell types. Though the process must carefully unfold over time to generate functional, well-adapted branching networks, we seldom hear about the time-based properties of angiogenesis, despite timing being central to other areas of biology. Here, we present a novel, time-based formulation of endothelial cell behaviour during angiogenesis and discuss a flurry of our recent, integrated in silico/in vivo studies, put in context to the wider literature, which demonstrate that tissue conditions can locally adapt the timing of collective cell behaviours/decisions to grow different vascular network architectures. A growing array of seemingly unrelated ‘temporal regulators’ have recently been uncovered, including tissue derived factors (e.g. semaphorins or the high levels of VEGF found in cancer) and cellular processes (e.g. asymmetric cell division or filopodia extension) that act to alter the speed of cellular decisions to migrate. We will argue that ‘temporal adaptation’ provides a novel account of organ/disease-specific vascular morphology and reveals ‘timing’ as a new target for therapeutics. We therefore propose and explain a conceptual shift towards a ‘temporal adaptation’ perspective in vascular biology, and indeed other areas of biology where timing remains elusive. This article is part of the themed issue ‘Systems morphodynamics: understanding the development of tissue hardware’

Electronic Supplementary Material from The temporal basis of angiogenesis

The process of new blood vessel growth (angiogenesis) is highly dynamic, involving complex coordination of multiple cell types. Though the process must carefully unfold over time to generate functional,well-adapted branching networks, we seldom hear about the time-based properties of angiogenesis, despite timing being central to other areas of biology. Here, we present a novel, time-based formulation of endothelial cell behaviour during angiogenesis and discuss a flurry of our recent, integrated in silico/in vivo studies, put in context to the wider literature, which demonstrate that tissue conditions can locally adapt the timing of collective cell behaviours/decisions to grow different vascular network architectures. A growing array of seemingly unrelated 'temporal regulators' have recently been uncovered, including tissue derived factors (e.g. semaphorins or the high levels of VEGF found in cancer) and cellular processes (e.g. asymmetric cell division or filopodia extension) that act to alter the speed of cellular decisions to migrate. We will argue that 'temporal adaptation' provides a novel account of organ/disease-specific vascular morphology and reveals 'timing' as a new target for therapeutics. We therefore propose and explain a conceptual shift towards a 'temporal adaptation' perspective in vascular biology, and indeed other areas of biology where timing remains elusive

The four largest synchronized groups of neurons at different times for <i>I</i> = 2.8 and <i>β</i> = 12.

<p>In each row, the first picture shows the coupling strength matrix and the four consecutive pictures show the largest synchronized clusters at that time. The first row corresponds to time <i>t</i> = 3810, and the time interval between each successive row is 10 units. Permanently and transiently synchronized clusters of neurons are clearly apparent.</p

The coupling strength matrix for <i>I</i> = 2.8 and <i>β</i> = 12 over a longer time interval.

<p>The picture at the top right is for time <i>t</i> = 3540. The time difference between successive pictures in each row is 10, and the time difference between successive rows is 130. The emergence of both permanent and transient strong couplings, resulting in either permanent or transient synchronization of the corresponding neurons, is apparent throughout the whole time interval studied.</p

The time variation in the order parameter <i>χ</i>(<i>t</i>) for <i>I</i> = 2.8 and <i>β</i> = 12.

<p>(a) The time series of <i>χ</i>(<i>t</i>) shows sustained variations between values close to 1, corresponding to high levels of synchronization, and values close to 0, corresponding to lower levels of synchronization. The continual variation of <i>χ</i>(<i>t</i>) results from the repeated transient synchronization of neurons in the network. (b) The power spectrum of <i>χ</i>(<i>t</i>) shows variations on a wide range of time scales, indicative of the complex dynamics apparent in the time series of <i>χ</i>(<i>t</i>). The large amplitude oscillation in <i>χ</i>(<i>t</i>) results in a peak in the power spectrum at <i>f</i> ≈ 20, while smaller amplitude, higher frequency, variations give a secondary peak at <i>f</i> ≈ 100. (c)-(f)The distributions of the complex numbers that define the order parameter on the unit circle in the complex plane at different times. At time <i>t</i> = 13 (shown in (c)) the system is largely unsynchronized, and subsequently evolves in time to successively more synchronized states at <i>t</i> = 3825 (shown in (d)), <i>t</i> = 3910 (shown in (e)), and <i>t</i> = 4000 (shown in (f)).</p

The time series and the Fourier power spectrum of the total coupling strength <i>K</i>(<i>t</i>) and the total membrane potential <i>X</i>(<i>t</i>) for <i>I</i> = 2.8 and <i>β</i> = 12.

<p>(a) The time series of <i>K</i>(<i>t</i>) showns continual variations between higher and lower total coupling strengths. (b) For <i>K</i>(<i>t</i>), the power <i>P</i>(<i>f</i>) associated with frequency <i>f</i> satisfies to a good approximation the power-law <i>P</i>(<i>f</i>) ∝ 1/<i>f</i>^<i>η</i>, where <i>η</i> = 2.628 ± 0.002, indicating that variations in <i>K</i>(<i>t</i>) occur on all time scales. The dashed line indicates the power-law relation. The large amplitude variation in the time series of <i>K</i>(<i>t</i>) result in a peak in the power spectrum at <i>f</i> ≈ 12, while the smaller amplitude, higher frequency, variations at the bottom of each large amplitude cycle give a secondary peak at frequency <i>f</i> ≈ 70. (c) The time series of <i>X</i>(<i>t</i>) also shows continual variations. (d) For <i>X</i>(<i>t</i>), the deviations of the power spectrum from a power-law are greater than for <i>K</i>(<i>t</i>), however, <i>X</i>(<i>t</i>) also shows variations on a wide range of time scales. The large amplitude oscillation in <i>X</i>(<i>t</i>) results in a peak in the power spectrum at <i>f</i> ≈ 20.</p

The Fourier power spectrum of the total coupling strength <i>K</i>(<i>t</i>) and the total membrane potential <i>X</i>(<i>t</i>) for small-world and scale-free networks for <i>I</i> = 2.8 and <i>β</i> = 12.

<p>(a) For <i>K</i>(<i>t</i>) on small-world networks with rewiring probability 0.3 the power <i>P</i>(<i>f</i>) associated with frequency <i>f</i> satisfies a power-law <i>P</i>(<i>f</i>) ∝ 1/<i>f</i>^<i>η</i>, where <i>η</i> = 2.013 ± 0.002 and <i>η</i> = 2.070 ± 0.002 for both mean degree 10 (red squares) and 20 (blue circles), respectively. (b) For <i>X</i>(<i>t</i>) on the same small-world networks as in (a) the deviations of the power spectrum from a power-law are greater than for <i>K</i>(<i>t</i>), however, <i>X</i>(<i>t</i>) also shows variations on a wide range of time scales. (c) For <i>K</i>(<i>t</i>) on scale-free networks <i>P</i>(<i>f</i>) satisfies a power-law <i>P</i>(<i>f</i>) ∝ 1/<i>f</i>^<i>η</i>, where <i>η</i> = 2.094 ± 0.002 and <i>η</i> = 2.028 ± 0.002 for both mean degree 10 (red squares) and 20 (blue circles), respectively. (d) For <i>X</i>(<i>t</i>) on the same scale-free networks as in (c) the deviations of the power spectrum from a power-law are greater than for <i>K</i>(<i>t</i>), however, <i>X</i>(<i>t</i>) also shows variations over a large range of time scales.</p